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A356927
E.g.f. satisfies A(x) = 1/(1 - x)^(A(x)/(1 - x)).
1
1, 1, 6, 54, 676, 10980, 220488, 5289592, 147828896, 4721152320, 169723566240, 6785559484704, 298726260001728, 14362141350822720, 748845960914596608, 42092072779399215360, 2537464961261745635328, 163317885950059143238656
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (-log(1-x)/(1-x))^k / k!.
E.g.f.: A(x) = exp( -LambertW(log(1-x)/(1-x)) ).
E.g.f.: A(x) = (1-x) * LambertW(log(1-x)/(1-x))/log(1-x).
a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (LambertW(exp(-1)) * exp(n - 1/2) * (1 - exp(1)*LambertW(exp(-1)))^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(-log(1-x)/(1-x))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(log(1-x)/(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-x)*lambertw(log(1-x)/(1-x))/log(1-x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 04 2022
STATUS
approved